Seekers of luxury living are lured from upscale coastal suburbs to the city, where Michelin-starred restaurants are leading a surge of creative endeavors

“Fifteen years ago, wealthy people didn’t live in Copenhagen,” says Danish architect Dan Stubbergaard. Instead, they were drawn north, to a cluster of attractive coastal suburbs nicknamed the Whiskey Belt.

That is changing now, as a vibrant restaurant scene helps to fuel a growing demand for high-end homes in the capital city and sparks a new wave of luxury development.

Klaus Kastbjerg, owner of Unionkul, a Copenhagen developer, cites the number and variety of restaurants, led by the world-famous Noma, as the city’s key selling point for relocating suburban buyers. Meanwhile, Copenhagen has become a major creative hub, setting trends in everything from architecture and television production to urban planning and subway design.

“The city is much more attractive than it was before,” adds Mr. Stubbergaard, founder of Cobe, a local architecture studio responsible for several new high-end apartment complexes.

Mr. Kastbjerg and Mr. Stubbergaard are collaborating on projects in transitioning districts. In Nordhavn, a northern harbor area in the process of a radical redevelopment, they are transforming the Silo, a 1950s concrete grain elevator, into a 17-story luxury high-rise that retains a rough, industrial feel. The 38 units will offer in-house concierge service and many will have private elevator access. Larger duplex units feature ceilings more than 23 feet high in the living and dining areas.

Set for completion next year, the building already has sold most of its units. One duplex on the 13th and 14th floors—with four bedrooms, two full baths and two half-baths—is listed for about $4.8 million.

Copenhagen’s residential real-estate prices have never been higher, says Troels Theill Eriksen, chief economist of DE, Denmark’s national organization of real-estate agents. The average price of residences has surpassed pre-crisis 2006 highs, he says. Between the fourth quarter of 2014 and first quarter of 2016, home prices overall in Copenhagen rose by 37.4%.

The largest gains were in some high-end districts. In leafy Østerbro, Copenhagen’s answer to Manhattan’s Upper East Side, for example, prices surged nearly 43%.

Even stronger gains were seen in Vesterbro, the hipster enclave behind Copenhagen’s main train station. A harborfront duplex apartment in there is listed for $2.7 million. The 2,400-square-foot unit has three bedrooms, three bathrooms, a double-height ceiling, and lavish water views.

Vesterbro lures home buyers in part because of the development of its Brooklyn-style 1930s Kødbyen, or meatpacking, complex, also home to several notable dining venues. Its pioneering restaurant is Kødbyens Fiskebar, a stylish bistro specializing in seafood. Locals revere the 7-year-old restaurant as a groundbreaker, helping to make dining out a regular event rather than a special occasion, as was the rule in Copenhagen until recently.

Christianshavn—the canal-lined, centuries-old neighborhood across the harbor from the city’s historic center—is another big draw. The area now offers a fair share of multimillion-dollar homes.

One development, the 105-unit Krøyers Plads, includes three contemporary brick buildings designed by Cobe and Vilhelm Lauritzen Architects. It sold out before completion in 2015. This month, a 2,518-square-foot unit, with two bedrooms and two baths, resold for $2.6 million.

The complex is next to Noma, which has helped build the area’s cachet. For years, the restaurant, opened in 2003, has been a leading contender for the title of top restaurant in the world, as named in the annual World’s 50 Best Restaurants list. Now, it is about to spread its goodwill, as it prepares to relaunch in 2017 in a new location a mile away.

Noma’s promotion of local ingredients and the rediscovery of cooking techniques has had an impact on the entire city. Copenhagen is now dotted by restaurants started by former Noma employees.

The 2016 Michelin guide to the Nordic countries gives a total of 20 stars to 16 Copenhagen restaurants, including the city’s first three-star venue, Østerbro’s Geranium, co-owned by Søren Ledet, a former Noma chef turned sommelier. A fixed menu paired with wines can cost about $500 a person.

Mr. Ledet says the city’s dining revolution dates roughly to 2011 and 2012, when Denmark began to make a tentative economic recovery from the crash of 2008 and 2009.

But he sees a synergy among all the city’s creative disciplines, not just its food. “I feel like everybody has got the same vision—to make Copenhagen the coolest place on earth,” he says.

In addition to Geranium, Østerbro also has Alchemist, a year-old restaurant that made it into the 2016 Michelin guide only a few months after opening. Alchemist’s 25-year-old chef, Rasmus Munk, serves quirky, dark humor with his $270, 45-course meals. The menu includes a lamb-brain mousse served in an edible “skull” of freeze-dried onion.

Food and real estate are on the minds of Østerbro residents Søren Garde, 53, and Rita Vibild, 56. In the past few years, “many cool food shops have opened, like organic butchers, bakeries and cheese shops,” says Mr. Garde, a furniture maker and founder of Garde Hvalsøe, a Copenhagen interior-design company.

Last year, he and his wife, a teacher, sold their Østerbro villa for $1.7 million, more than doubling their 2004 investment on the purchase and renovation of the home. They relocated to a nearby 2,100-square-foot apartment, paying $942,000 for the property. They spent another $374,000 on renovations, knocking down several walls to create a zigzag open plan and three bedrooms.

The couple and their two children—Gustav, 16, and Nanna, 14—plan to stay in the new home about five years, while Mr. Garde finalizes plans for the $2.4 million purchase and renovation of another nearby property.

The couple want to turn their next home into a rooftop urban farm, with a network of vegetable gardens and greenhouses.

Even food trucks are helping to transform certain neighborhoods. The once-isolated Papirøen, or “paper island,” now has a network of new bridges and temporary attractions that have allowed it to become a point of pilgrimage for local foodies. They are flocking to an upscale collection of indoor food trucks called Copenhagen Street Food. Vendors sell a variety of dishes, from American barbecue to South Korean barbecue to Danish standbys such as smørrebrød, a traditional open-face sandwich.

In two years’ time, the whole island is set for redevelopment, anchored by hundreds of luxury apartments. Prices may reach $1,390 per square foot, says Cobe’s Mr. Stubbergaard, whose firm has created the master plan for the project.

Kirsa Hage and Lasse Schmidt are getting ready to trade in the traditional Copenhagen coziness of Østerbro for Nordhavn. With one daughter away from home and a son moving out in the next few years, they are planning to move into the Silo as an empty-nester refuge.

The couple, who run a company that creates subtitles for Danish films and television, have lived in a rent-controlled apartment for 19 years—a 1,936-square-foot flat with four bedrooms, for which they pay about $1,500 a month.

In the Silo, they paid $1.1 million for a 1,400-square-foot, seventh-floor apartment with three bedrooms and one bathroom, and featuring light-filled southern and western exposures. They expect to move in the spring.

“We think of it as a good investment,” says Ms. Hage, 51. Although the area feels somewhat isolated now, a planned 2019 extension of the city’s metro network will connect Nordhavn to the rest of the city and its beckoning restaurants.

Ms. Hage and Mr. Schmidt, 48, make a point of visiting local Michelin-starred restaurants on occasion. People in Copenhagen, she says, like to talk about food, the main topic of conversation often being “the last restaurant you went to.”